UNIVERSITY OF MAINE AT FARMINGTON COLLEGE OF EDUCATION, HEALTH AND REHABILITATION
LESSON PLAN FORMAT
Teacher’s Name: Mr. Potter Lesson # 6:Facet: Empathy
Grade Level: FreshmanNumbers of Days: 3 +
Topic: The use of Properties, and the Order of Operations in order to solve linear equations
PART I:
Objectives
Student will understand that
Students will understand that using PMDAS (Parentheses, multiplication, division, addition, and subtraction) and other order of operations skills are essential to solving problems.
Student will know
Students will know distributive, associative, and commutative properties.
Student will be able to do
Students will be able to take suggestions from their peers to further their own understandings.
Product:Blogger, Google SketchUp
Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment
Common Core State Standards:
Content Area: Algebra
Grade Level: High School
Domain: Creating Equations
Cluster: Create equations that describe numbers or relationships.
Standards(s): 1. Create equations and inequalities in one variable and use them to solve problems.
Rationale:
Student will meet this standard by applying real world applications. With these applications they will create equations and inequalities with the use of PMDAS, the Commutative property, the Associative Property, and the Distributive Property, and solve them.
Assessments
Formative (Assessment for Learning)
Section I – checking for understanding during instruction
Students will ask one last question before leaving class. They will be asked to post this question in their blog. They will first present the question, and then try to answer is. Students are encouraged to use any resource needed to answer this question. Next class, students will report out their question, and their answer.
Section II – timely feedback for products (self, peer, teacher)
Students will then use Blogger to first present their question, and second to answer that question involving the order of operations and the three properties. Students will spend time collaborating with their classmates, and having discussions about their questions, and answers.
Summative (Assessment of Learning):
Blogger: Students will discuss and reflect on questions they may have remaining from class. Students will then post a blog entry using Blogger technology. They will post their questions on Blogger, and attempt to answer their own question using multiple resources. These resources are limitless. The web, parents, textbook, friends, or maybe even another teacher, are good reference ideas. This will be an ongoing project throughout the unit. You will be graded on your participation, and work ethic. (40 Points)
Integration
Technology:
Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive)
Content Areas:
Art: Students will be able to use different colors, fonts and layouts to allow their artistic creativity to come alive through Blog.
English: Students will use English to reflect on their questions and thoughts. They will have to incorporate certain math vocabulary, and may have to use a dictionary to find definitions.
Groupings
Section I - Graphic Organizer & Cooperative Learning used during instruction
Students will know the PMDAS (order of operations) and the three properties (associative, commutative, and distributive). Students will use a Flow Chart (Graphic Organizer) and the Mix-Pair-Freeze cooperative learning activity to ponder their ideas and questions for their Blogs.
Section II – Groups and Roles for Product
Students will use the Mix-Pair-Freeze cooperative learning activity, and their Flow Chart graphic organizer to collect all their thoughts and ideas for their Blogs. Their Blog must include the use of PMDAS (order of operations) and the three properties (associative, commutative, and distributive). Students will be randomly switching partners during the Mix-Pair-Freeze activity. Students may pick one partner to work with while they work on their flow charts.
Differentiated Instruction
MI Strategies
Verbal: Students will verbally tell the teacher their One Last Question before leaving class. This question should relate to one of the three properties: distributive, associative, or commutative.
Logic: Student will be forced to really think about their question relating to one of the three properties: distributive, associative, or commutative in a blog entry on Blogger.
Visual: The teacher will visually show PMDAS during class to help students further understand the three properties: distributive, associative, or commutative.
Intrapersonal: Student will individually work on their blog entry as homework. Here they will present a question on one of the three properties: distributive, associative, or commutative and try to answer their own question prior to the next class period.
Interpersonal: Students will interact with a friend, parent, or even another teacher to try and find the answer to their question relating to one of the three properties: distributive, associative, or commutative.
Naturalist: In the blogs, students will be encouraged to create a story, in nature using the three properties.
Modifications/Accommodations
From IEP’s (Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan)I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.
Plan for accommodating absent students:
Student who are absent from this lesson will be required to make up the work. They will check the online page to get the assignments. If students know they will be missing a lesson they should notify me as soon as possible, so we can make arrangements, for work to keep to up to date. Students are encouraged to converse with their peers to get help with assignments. For hard copy assignments that are not online students will be able to briefly stop in upon returning to school to pick up the missed work. They will be allotted three days to complete the given work. For the lessons that they miss, there will be links posted online to re-enforce, or re-teach what was taught that day. Kids who miss class are encouraged to email me with any remaining questions concerning their assignment(s). Also, students will be referred to the math-learning center, for extra instruction and assistance!
Extensions
Type II technology:
Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive). This is a type two technology because Blogger has amazing capabilities. Blogger can present materials in cool, colorful, and individual ways. It creates a sense of structured flow for the students. Students will benefit from Blogger technology because it will allow them to be creative, and they will have the opportunity to work at their own pace, and own ability. Students will be given the opportunity to think, analyze, and present their Blog reflections on the topic of PMDAS (the order of operations) and the three properties (associative, commutative, and distributive)
Gifted Students:
I will give gifted students the opportunity to reflect in their Blog using more advanced problems. Students will have to have fully interpreted the content in Blogs so this will help challenge the gifted students to go above and beyond the normal expectations.
http://linearequationsinreallife.weebly.com/ Students will begin exploring this WebQuest, and working through it individually. This will provide as the final assessment in the unit.
PART II:
Teaching and Learning Sequence(Describe the teaching and learning process using all of the information from part I of the lesson plan)Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages)
The room will be set up with desks arranged in groups of four, side by side.
Day One: Linear Equations with Properties, and Order of Operations (80 Minutes)
Introduction: Overview of class schedule, and intro of lesson (5 minutes)
(Hook): Start class by telling a story that uses distributive, associative, and commutative properties in real life. (5 Minutes)
Instructional Period: Present Properties, and Order of Operations. Introduce Blogger and show instructional video:
First Class Activity: Student will work with the Mix-Pair-Freeze cooperative learning activity. They will begin discussing their ides. They will collaborate and decide what they ideas they want to cove in the Blog.(10 Minutes)
Second Class Activity: Students will, in their partners of choice use a Flow chart graphic organizer to come up with several options for their Blogger. They will present a question and work down the steps in the correct order. This will be a good way for them to organize their math questions.(30 Minutes)
Task Introduction: Students will be asked to use Blogger. Upon arriving to the next class they will each share one question they had, as well as where, and how they found the answer. They will also provide one unique thing they have incorporated into their blogs through themes, fonts, back rounds, etc.(5 Minutes)
Day Two: Blogs onLinear Equations with Properties, and the Order of Operations (80 Minutes)
Introduction: The class will briefly review the task assignment to get everyone thinking about their Blogs. Students will all share one thing from their Blog that they learned or liked. Also during this time the teacher will briefly review properties, solutions, and the order of operations.(20 Minutes)
Work Period: Students will work together to create an addition blog entry using properties, and the order of operations. The teacher will roam and help students with question, and give helpful suggestions to each group.(20 Minutes)
Break: Students will take a five-minute break, to socialize and hopefully talk to other piers to compare ideas! The teacher will give students a hint as to collaborate with each other during this time period.(5 Minutes)
Second Work Period: (15Minutes)
Report Out: Students will share their new questions, and answers and provide on example in which it is real world applicable(20 Minutes)
Day 3: Final Assessment Introduction (80 Minutes)
Introduction: Introduce WebQuest, Explain what a WebQuest is and why the students will be participating in one themselves.(15 Minutes)
Hook:Weebly Introduction (5 Minutes)
Exploration and Review: Students will explore the WebQuest and begin to grasp what they will be doing through this Weebly! Students will review previous content, graphic organizers, cooperative learning activities, formative assessments, summative assessments, and other resources. (35 Minutes)
Walk Through: The teacher will walk through the Weebly with the class, and break it down. Questions will be answered and the completion of the WebQuest will begin!(20 Minutes)
Assignment: Students will be asked to download the Google Sketch up program, and begin exploring and playing with some ideas. Also students will look into bridge structures, and come up with some ideas for their 3-Dimensional bridges, Next class the students will continue to work through the Weebly.
The class will be arranged in groups of two. The desks will be placed side-by-side facing the front of the classroom. This will allow for normal instruction, like any other day, but also set allow for an easier transition when groups are formed. Desks will already be in place so the transition time will be far faster. The agenda is pretty simple; it will be made up of three class periods. This first day the teacher will present the lesson on properties, and the order of operations and allow students to chose their own partner. Once in groups the students will watch an intro video on how to use Blogger, and then they will participate in Mix-Pair-Freeze cooperative learning activity, and Flow Chart graphic organizer worksheet. On the second day students will all share one thing that they learned while exploring Blogger technology. A short time will be taken to reteach the content from the previous class, to help struggling students further understand the content. They will then work with their partners to come up with another question to present, and answer using their Blogs. Students will then have a work period. They will be given a break in the middle of the class work period to re motivate themselves. At the end of class, Students will report to the class what their question was, and how they solved it. Finally on the third and last day the students will be introduced to WebQuests. They will be hooked by being introduced to the introduction of the class Weebly. Students will then explore the WebQuest and begin to grasp what they will be doing through this Weebly! Students will review previous content, graphic organizers, cooperative learning activities, formative assessments, summative assessments, and other resources. The teacher will walk through the Weebly with the class, and break it down toward the end of class. Questions will be answered and the completion of the WebQuest will begin! Students will be asked to download the Google Sketch up program, and begin exploring and playing with some ideas. Also students will look into bridge structures, and come up with some ideas for their 3-Dimensional bridges, Next class the students will continue to work through the Weebly.
Students will know properties, PMDAS, and solutions. Students will use Mix-Pair-Freeze (Cooperative learning activity) and Flow Chart (Graphic organizer) to start organizing thoughts they have for their Blogs. As the teacher I will deliver a short and to the point instruction of twenty five minutes. In this time I will be able to effectively cover the needed material. Along the way I will ask question to all my students and they will be actively involved by participating in On Last Question. Based on the feedback I receive, I will be able to retouch on certain things and present them in multiple ways until all my students understand each though process. I will easily be able to check for understanding using one last question and I will be able to do it constantly throughout my instructional period. Students can refer back to previous organizers, and learning activities used throughout the unit, and reuse them for assistance while working with the WebQuest. The content of the overall unit is as follows:
Equation: Students may have a general idea of what equations are. An equation is a something that shows, in terms of math, that two things are equal to one another. The statement 60=30+30 is an equation. It is important that students know that both sides of an equation are the same but are simply written in different ways.
Linear equations: are equations that have an unknown variable like (x, y, z), these variables are all of the power 1. This is the most important thing to linear equations. The variable can only be raised to the power of one. A variable to power 2 like (Y2) is not a linear equation because it has an exponent that is not equal to one. 60=20+x is a linear equation.
Irrational Numbers:are numbers that are not integers, whole numbers, or fractions. Instead they are decimals that have an ongoing decimal with NO pattern. For example: 3.3257689475635241639506. There is no pattern therefore it is irrational. The mathematical symbol pi, is a great example of an irrational number.
Rational Numbers: Rational numbers are alike whole numbers, but also include fractions, and decimals. If a decimal has a repeating number such as, 6.6444444444 then it is indeed rational! Repeating decimals are rational, not irrational!
Whole Numbers: wholes numbers are and number that is not a fraction, and is not negative.
Example: {0, 1, 2, 3, 4, 5, .... Infinity}
Integers: Integers are like whole numbers in the fact that they cannot be fractions. They can however be negative.
Real Numbers: Real numbers include decimals, fractions, whole numbers, integers, irrational numbers, and rational numbers.
Variables: A variable is an unknown value usually expressed by (x, or y). Knowing that equations are two things that are equal, we sometimes have an unknown value. We express this unknown with a variable. In they equation 4X+ 8= 16, X is our variable.
Constants: constants are numbers with in an equation that stand-alone. In the equation, 12X + 20 = 80, the constants are 20, and 80. 12 is not a constant because it is tied to the X. In this case 12 is considered a coefficient. Constants can also be letters that stand for a fixed number. Most formulas us letters as constants because they can stand for any real number. In the slope-intercept form, Y= mx + b, the constants are Y, and b. m again being tied to a variable (x) is a coefficient.
PMDAS (Order of Operations):
Is also know as please excuse my dear aunt sally. This acronym is a popular way to remember these steps. They stand for doing things in a certain order when solving equations. PMDAS stands for:
This property states that you can add or subtract things in any certain order, as well as multiply things in any order.
Examples:
Addition/Subtraction 5 + 8 - 4 = 5 - 4 + 8
Multiplication: 5 x 8 x 4 = 4 x 5 x 8
Associative:
This property states that both multiplication and addition can be two numbers at a time. With addition you can group these numbers in any way, and still get the same answer. With multiplication we can group numbers in a product in any way, and still get the same answer.
Examples:
Addition: (5x + 3x) + 8x = 5x + (8x + 3x)
Multiplication: 2x2(3y) = 3y(2x2)
Distributive:
This property occurs when you are dealing with both multiplication and addition. It tells us that if a term is multiplied by other terms within a set of parenthesis, then we need to "distribute" the multiplying term by all the terms within the parenthesis.
Example: 6(5x + 4)= 30x + 24
Solutions: When dealing with variables that are not to the first power, there may be multiple solutions (answers) for that variable.
Example:
x2-5x +6=0 This reduces to (x - 3) and (x - 2) = 0 which gives us the solutions of x = 3, and x = 2
Inequalities:
An inequality is a mathematical sentence that compares two quantities that do not equal each other, or may possibly equal one another. There are a four main ways to compare quantities: > (Greater than)
< (Less than)
< (Less than, or equal to)
> (Greater than, or equal to)
An example of this is 20 + 39 < 97-22 This is saying that 20 + 39 is less than 97- 22
To check that this is true, you solve both sides separately which will make this 59 < 65 which saying that 59 is less than 65 which is correct.
Another example of this is 5 x 10 > 32 + 18 this is saying that 5 x 10 is greater than or equal to 32 + 18.
To check this we again solve both sides separately. We get 50 > 50. so in this case they are equal. (50 = 50)
Slope – Intercept Form:
The slope - intercept form of a linear equation is given by the following formula: y= mx + b
‘m’ is the slope and ‘b’ is the y – intercept)
Slope is a ratio use to measure the steepness of a line. To find slope you must find the change in ‘y’ over the change in ‘x’. This can also be written as: Rise/Run
The way to find rise/run is to have to points on a line. For example (5,8) and (10,12); to find the ‘rise’ you find the difference between the y coordinates. So; 12 – 8 = 4 then you do the same thing for the x coordinates to find the ‘run’. So; 10 - 5 = 5 this will make the final answer be 4/5. Our slope is 4/5ths the equation for this is: Y1 - Y / X1- X
Perimeter: To find the perimeter of a 2D shape you must add up all the sides of that shape. For example, if a rectangle had side lengths of 5, 7, 5, and 7, we would add up every side to get our perimeter. 5+7+5+7= 24. So, the perimeter is 24.
Area: Area is the amount of surface space of a 2D shape. It is measured in square units. The area can me measured in multiple ways such as Centimeters, inches, feet, meters, millimeters, and more.
To find the area we simply multiply the length of a shape by its width. For example if we had a rectangle with a side length of 8 and a width of 12 our area would be 96. We got that by multiplying 8 X 12 = 96
Students will use Mix-Pair-Freeze (Cooperative learning activity) and Flow Chart (Graphic organizer) to start organizing thoughts they have for their Blogs. Students will use these activities for assistance. Their Blog must include the use of properties, and the order of operations. The teacher will use One Last Question to check for understanding. Students will write down one question they have, or something that may be unclear. Students will then use Blogger to create a blog using linear and quadratic equations. Student will spend class time with their partner to work with Blogger. They should be prepared to report their questions and answers at the ends of class. The teacher will roam the classroom providing answers to questions and helping students with their Blogs. Students must collaborate their ideas with the teachers before full creation, and presentation. Students will both help to come up with ideas, during the creation of math problems using properties, order of operations, and they will both help to creatively incorporate it all into Blogger. On the third day students will be introduced to WebQuests. During this class period students will tie up loose ends with their Blogs, and begin reviewing, recalling, and rethinking about all the things that were covered in this unit. They can refer to the process section of the Weebly to achieve this.
Students will self-assess during their rethink/ refine stage in the final assessment. They will go down through the rubrics that they have been given. They will grade themselves, and add or fix anything that they missed or feel they may improve on. During the class presentations I will grade them on the same rubrics. I will also grade them based on the effort, participation, and quality of their work. At the end of all the presentations I will hand back these checklists along with a small written reflection. They will all receive their grades immediately after all the gallery walk is over. I will address the class overall and then talk to each group that has questions or comments. This will all pertain to their homework because they will be given problems from their book on the exact same material. In the following classes they will be given a pre- quiz, and finally a quiz. This lesson content will combine with other contents, and students will be assessed on multiple lesson contents at the end of the unit. Evaluate, Tailors: Verbal, Interpersonal, Intrapersonal, Logical
Develop detailed content notes so a substitute or a colleague can teach your lesson. (2-3 pages)
Equation: Students may have a general idea of what equations are. An equation is a something that shows, in terms of math, that two things are equal to one another. The statement 60=30+30 is an equation. It is important that students know that both sides of an equation are the same but are simply written in different ways.
Linear equations: are equations that have an unknown variable like (x, y, z), these variables are all of the power 1. This is the most important thing to linear equations. The variable can only be raised to the power of one. A variable to power 2 like (Y2) is not a linear equation because it has an exponent that is not equal to one. 60=20+x is a linear equation.
Irrational Numbers:are numbers that are not integers, whole numbers, or fractions. Instead they are decimals that have an ongoing decimal with NO pattern. For example: 3.3257689475635241639506. There is no pattern therefore it is irrational. The mathematical symbol pi, is a great example of an irrational number.
Rational Numbers: Rational numbers are alike whole numbers, but also include fractions, and decimals. If a decimal has a repeating number such as, 6.6444444444 then it is indeed rational! Repeating decimals are rational, not irrational!
Whole Numbers: wholes numbers are and number that is not a fraction, and is not negative.
Example: {0, 1, 2, 3, 4, 5, .... Infinity}
Integers: Integers are like whole numbers in the fact that they cannot be fractions. They can however be negative.
Example: {Negative Infinity......., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ......... Infinity}
Real Numbers: Real numbers include decimals, fractions, whole numbers, integers, irrational numbers, and rational numbers.
Variables: A variable is an unknown value usually expressed by (x, or y). Knowing that equations are two things that are equal, we sometimes have an unknown value. We express this unknown with a variable. In they equation 4X+ 8= 16, X is our variable.
Constants: constants are numbers with in an equation that stand-alone. In the equation, 12X + 20 = 80, the constants are 20, and 80. 12 is not a constant because it is tied to the X. In this case 12 is considered a coefficient. Constants can also be letters that stand for a fixed number. Most formulas us letters as constants because they can stand for any real number. In the slope-intercept form, Y= mx + b, the constants are Y, and b. m again being tied to a variable (x) is a coefficient.
PMDAS (Order of Operations):
Is also know as please excuse my dear aunt sally. This acronym is a popular way to remember these steps. They stand for doing things in a certain order when solving equations. PMDAS stands for:
Properties: Commutative:
This property states that you can add or subtract things in any certain order, as well as multiply things in any order.
Examples:
Addition/Subtraction 5 + 8 - 4 = 5 - 4 + 8
Multiplication: 5 x 8 x 4 = 4 x 5 x 8
Associative:
This property states that both multiplication and addition can be two numbers at a time. With addition you can group these numbers in any way, and still get the same answer. With multiplication we can group numbers in a product in any way, and still get the same answer.
Examples:
Addition: (5x + 3x) + 8x = 5x + (8x + 3x)
Multiplication: 2x2(3y) = 3y(2x2)
Distributive:
This property occurs when you are dealing with both multiplication and addition. It tells us that if a term is multiplied by other terms within a set of parenthesis, then we need to "distribute" the multiplying term by all the terms within the parenthesis.
Example: 6(5x + 4)= 30x + 24
Solutions: When dealing with variables that are not to the first power, there may be multiple solutions (answers) for that variable.
Example:
x2-5x +6=0 This reduces to (x - 3) and (x - 2) = 0 which gives us the solutions of x = 3, and x = 2
Inequalities:
An inequality is a mathematical sentence that compares two quantities that do not equal each other, or may possibly equal one another. There are a four main ways to compare quantities:
> (Greater than)
< (Less than)
< (Less than, or equal to)
> (Greater than, or equal to)
An example of this is 20 + 39 < 97-22 This is saying that 20 + 39 is less than 97- 22
To check that this is true, you solve both sides separately which will make this 59 < 65 which saying that 59 is less than 65 which is correct.
Another example of this is 5 x 10 > 32 + 18 this is saying that 5 x 10 is greater than or equal to 32 + 18.
To check this we again solve both sides separately. We get 50 > 50. so in this case they are equal. (50 = 50)
Slope – Intercept Form:
The slope - intercept form of a linear equation is given by the following formula: y= mx + b
‘m’ is the slope and ‘b’ is the y – intercept)
Slope is a ratio use to measure the steepness of a line. To find slope you must find the change in ‘y’ over the change in ‘x’. This can also be written as: Rise/Run
The way to find rise/run is to have to points on a line. For example (5,8) and (10,12); to find the ‘rise’ you find the difference between the y coordinates. So; 12 – 8 = 4 then you do the same thing for the x coordinates to find the ‘run’. So; 10 - 5 = 5 this will make the final answer be 4/5. Our slope is 4/5ths the equation for this is: Y1 - Y / X1- X
Perimeter: To find the perimeter of a 2D shape you must add up all the sides of that shape. For example, if a rectangle had side lengths of 5, 7, 5, and 7, we would add up every side to get our perimeter. 5+7+5+7= 24. So, the perimeter is 24.
Area: Area is the amount of surface space of a 2D shape. It is measured in square units. The area can me measured in multiple ways such as Centimeters, inches, feet, meters, millimeters, and more.
To find the area we simply multiply the length of a shape by its width. For example if we had a rectangle with a side length of 8 and a width of 12 our area would be 96. We got that by multiplying 8 X 12 = 96
Handouts
List the items that need to be printed out for the lesson.
Rubrics for WebQuest (60 copies)
Flow Chart graphic organizer (60 copies front and back)
ALL OTHER HANDOUTS CAN BE FOUNF ON THE WEBQUEST.
Maine Common Core Teaching Standards for Initial Teacher Certification and Rationale Standard 1 –Learner Development. The teacher understands how learners grow and develop,recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.
Learning Styles Clipboard: The clipboard students in my class will have graphic organizers in order to help the students organize step-by-step their logic and ideas. The class period is clearly planned out on the board so students can see how long we will be doing each thing in class. Students will be given a handout, and rubrics that will provide my expectations. This will help them to understand exactly what they are to do.
Microscope: The microscopes in my class will be able to have in depth conversations while they create their final products using all the content from the unit. They will be able to solve problems alike in their textbooks, which will further expand their understandings.
Puppy: For my puppy student I will ensure that they are receiving extra supportive and assistance from myself to make thing more easy going. This will help them feel like they are working and learning in a fun, and safe environment. These students will be able to collaborate with their peers in the classroom as well. The students will have multiple planned times to meet with me and talk about the project.
Beach Ball: For my beach ball learners I will provide them with options, and let them use whatever tools they feel will help them complete the project. Students will be placed with another student who will likely motivate and interest their partner while using Blogger, and Google SketchUp technology. They will be able to present one section of their final product if they desire and present the rest to the teacher at another time. All the beach ball learners will participate in cooperative learning activities, and graphic organizers with their partners. Here they will be heard, and they will feel as if they can speak freely.
Rationale: Students will be able to experience all of the learning styles in this project. Students and the teacher will realize how other students need information, or even that some students require a higher comfort level. This will allow for a judge free, respectful classroom for all students so that they can reach their highest abilities.
Standard 6 -Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their on growth,to monitor learner progress, and to guide the teacher's and learner's decision making.
Formative (Assessment for Learning)
Section I – checking for understanding during instruction
Students will ask one last question before leaving class. They will be asked to post this question in their blog. They will first present the question, and then try to answer is. Students are encouraged to use any resource needed to answer this question. Next class, students will report out their question, and their answer.
Section II – timely feedback for products (self, peer, teacher)
Students will then use Blogger to first present their question, and second to answer that question involving the order of operations and the three properties. Students will spend time collaborating with their classmates, and having discussions about their questions, and answers.
Summative (Assessment of Learning):
Blogger: Students will discuss and reflect on questions they may have remaining from class. Students will then post a blog entry using Blogger technology. They will post their questions on Blogger, and attempt to answer their own question using multiple resources. These resources are limitless. The web, parents, textbook, friends, or maybe even another teacher, are good reference ideas. This will be an ongoing project throughout the unit. You will be graded on your participation, and work ethic. (40 Points)
Standard 7-Planning Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum,cross-disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.
Content Knowledge:
See Content Notes
MLR or CCSS:
Common Core State Standards:
Content Area: Algebra
Grade Level: High School
Domain: Creating Equations
Cluster: Create equations that describe numbers or relationships.
Standards(s): 1. Create equations and inequalities in one variable and use them to solve problems.
Facet:Empathy, Explanation, Application, Perspective, Interpretation, and Self-Knowledge
Rationale:
Student will meet this standard by applying real world applications. With these applications they will create equations and inequalities with the use of:
Standard 8 -Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.
MI Strategies:
Verbal: Students will verbally tell the teacher their One Last Question before leaving class. This question should relate to one of the three properties: distributive, associative, or commutative.
Logic: Student will be forced to really think about their question relating to one of the three properties: distributive, associative, or commutative in a blog entry on Blogger.
Visual: The teacher will visually show PMDAS during class to help students further understand the three properties: distributive, associative, or commutative.
Intrapersonal: Student will individually work on their blog entry as homework. Here they will present a question on one of the three properties: distributive, associative, or commutative and try to answer their own question prior to the next class period.
Interpersonal: Students will interact with a friend, parent, or even another teacher to try and find the answer to their question relating to one of the three properties: distributive, associative, or commutative.
Naturalist: In the blogs, students will be encouraged to create a story, in nature using the three properties.
Type II Technology: Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive). This is a type two technology because Blogger has amazing capabilities. Blogger can present materials in cool, colorful, and individual ways. It creates a sense of structured flow for the students. Students will benefit from Blogger technology because it will allow them to be creative, and they will have the opportunity to work at their own pace, and own ability. Students will be given the opportunity to think, analyze, and present their Blog reflections on the topic of PMDAS (the order of operations) and the three properties (associative, commutative, and distributive) Rationale: This lesson was designed in such a way where differentiation can be used, to fit the needs of all students. All Multiple Intelligences were kept in mind during the process, and resources are provided for the students. During this lesson students will be able to work their strong intelligences as well as work on some of their weaker ones. They will also be able to use the technology, and multiple resources to the advantage of helping them to reach a higher, more enjoyable learning level.
NETS STANDARDS FOR TEACHERS
1. Facilitates and Inspire Student Learning and Creativity. Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments. a. Promote, support, and model creative and innovative thinking and inventiveness
b. Engage students in exploring real-world issues and solving authentic problems using digital tools and resources
c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes
d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in face-to-face and virtual environments
Rationale: Students will be working with Blogger and Google SketchUp in order to create a new way to ask and answer questions, and create 3-Dimensional structures using mathematics. Students can use this technology to share information with their peers while working. The lesson is geared to the fact that students will be working together in order to understand the information. Two brains are better than one. This will help the overall learning and progress of the students. Students will also be learning the content material through repetition, and applying that knowledge when using Blogger and Google SketchUp.
2. Design and Develop Digital Age Learning Experiences and Assessments. Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop knowledge, skills, and attitudes identified in the NETS-S.
a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity
b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants in setting their own educational goals, managing their own learning, and assessing their own progress
c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources
d. Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching
Rationale: Students will be using Blogger and Google SketchUp as a way to explore new intelligences and build further on their stronger intelligences. Students will have opportunities to relate information to their learning style of choice, whether it is interpersonal, intrapersonal, visual, or even logic. They will have opportunities to work in groups, and individually. A number of tasks and activities will be given to the students to help them understand the information. They will be able to practice, use graphic organizers, rubrics, cooperative learning activities, and will have multiple chances to meet with the teacher and collaborate with their peers. They will have a final product that they will present to the class, which will show whether or not the student has mastered the material.
COLLEGE OF EDUCATION, HEALTH AND REHABILITATION
LESSON PLAN FORMAT
Teacher’s Name: Mr. Potter Lesson # 6:Facet: Empathy
Grade Level: FreshmanNumbers of Days: 3 +
Topic: The use of Properties, and the Order of Operations in order to solve linear equations
PART I:
Objectives
Student will understand that
Students will understand that using PMDAS (Parentheses, multiplication, division, addition, and subtraction) and other order of operations skills are essential to solving problems.
Student will know
Students will know distributive, associative, and commutative properties.
Student will be able to do
Students will be able to take suggestions from their peers to further their own understandings.
Product:Blogger, Google SketchUp
Maine Learning Results (MLR) or Common Core State Standards (CCSS) Alignment
Common Core State Standards:
Content Area: Algebra
Grade Level: High School
Domain: Creating Equations
Cluster: Create equations that describe numbers or relationships.
Standards(s): 1. Create equations and inequalities in one variable and use them to solve problems.
Rationale:
Student will meet this standard by applying real world applications. With these applications they will create equations and inequalities with the use of PMDAS, the Commutative property, the Associative Property, and the Distributive Property, and solve them.
Assessments
Formative (Assessment for Learning)
Section I – checking for understanding during instruction
Students will ask one last question before leaving class. They will be asked to post this question in their blog. They will first present the question, and then try to answer is. Students are encouraged to use any resource needed to answer this question. Next class, students will report out their question, and their answer.
Section II – timely feedback for products (self, peer, teacher)
Students will then use Blogger to first present their question, and second to answer that question involving the order of operations and the three properties. Students will spend time collaborating with their classmates, and having discussions about their questions, and answers.
Summative (Assessment of Learning):
Blogger: Students will discuss and reflect on questions they may have remaining from class. Students will then post a blog entry using Blogger technology. They will post their questions on Blogger, and attempt to answer their own question using multiple resources. These resources are limitless. The web, parents, textbook, friends, or maybe even another teacher, are good reference ideas. This will be an ongoing project throughout the unit. You will be graded on your participation, and work ethic. (40 Points)
Integration
Technology:
Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive)
Content Areas:
Art: Students will be able to use different colors, fonts and layouts to allow their artistic creativity to come alive through Blog.
English: Students will use English to reflect on their questions and thoughts. They will have to incorporate certain math vocabulary, and may have to use a dictionary to find definitions.
Groupings
Section I - Graphic Organizer & Cooperative Learning used during instruction
Students will know the PMDAS (order of operations) and the three properties (associative, commutative, and distributive). Students will use a Flow Chart (Graphic Organizer) and the Mix-Pair-Freeze cooperative learning activity to ponder their ideas and questions for their Blogs.
Section II – Groups and Roles for Product
Students will use the Mix-Pair-Freeze cooperative learning activity, and their Flow Chart graphic organizer to collect all their thoughts and ideas for their Blogs. Their Blog must include the use of PMDAS (order of operations) and the three properties (associative, commutative, and distributive). Students will be randomly switching partners during the Mix-Pair-Freeze activity. Students may pick one partner to work with while they work on their flow charts.
Differentiated Instruction
MI Strategies
Verbal: Students will verbally tell the teacher their One Last Question before leaving class. This question should relate to one of the three properties: distributive, associative, or commutative.
Logic: Student will be forced to really think about their question relating to one of the three properties: distributive, associative, or commutative in a blog entry on Blogger.
Visual: The teacher will visually show PMDAS during class to help students further understand the three properties: distributive, associative, or commutative.
Intrapersonal: Student will individually work on their blog entry as homework. Here they will present a question on one of the three properties: distributive, associative, or commutative and try to answer their own question prior to the next class period.
Interpersonal: Students will interact with a friend, parent, or even another teacher to try and find the answer to their question relating to one of the three properties: distributive, associative, or commutative.
Naturalist: In the blogs, students will be encouraged to create a story, in nature using the three properties.
Modifications/Accommodations
From IEP’s (Individual Education Plan), 504’s, ELLIDEP (English Language Learning Instructional Delivery Education Plan)I will review student’s IEP, 504 or ELLIDEP and make appropriate modifications and accommodations.
Plan for accommodating absent students:
Student who are absent from this lesson will be required to make up the work. They will check the online page to get the assignments. If students know they will be missing a lesson they should notify me as soon as possible, so we can make arrangements, for work to keep to up to date. Students are encouraged to converse with their peers to get help with assignments. For hard copy assignments that are not online students will be able to briefly stop in upon returning to school to pick up the missed work. They will be allotted three days to complete the given work. For the lessons that they miss, there will be links posted online to re-enforce, or re-teach what was taught that day. Kids who miss class are encouraged to email me with any remaining questions concerning their assignment(s). Also, students will be referred to the math-learning center, for extra instruction and assistance!
Extensions
Type II technology:
Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive). This is a type two technology because Blogger has amazing capabilities. Blogger can present materials in cool, colorful, and individual ways. It creates a sense of structured flow for the students. Students will benefit from Blogger technology because it will allow them to be creative, and they will have the opportunity to work at their own pace, and own ability. Students will be given the opportunity to think, analyze, and present their Blog reflections on the topic of PMDAS (the order of operations) and the three properties (associative, commutative, and distributive)
Gifted Students:
I will give gifted students the opportunity to reflect in their Blog using more advanced problems. Students will have to have fully interpreted the content in Blogs so this will help challenge the gifted students to go above and beyond the normal expectations.
Materials, Resources and Technology
List all the items you need for the lesson.
Computers
Calculators
Projector
Library
Google (internet browsers)
Blogger Account
Flow Chart (Graphic Organizer)
Mix-Pair-Freeze (Cooperative learning activity)
Source for Lesson Plan and Research
List all URL and describe.
http://www.blogger.com/ Students will use Blogger to reflect on their ideas, and questions.
http://www.youtube.com/watch?v=rKVQKQxxUlk Students will watch this tutorial on how to use Blogger.
http://www.eduplace.com/graphicorganizer/pdf/flow.pdf Students will use this flow chart graphic organizer to collaborate ideas and answers to their questions.
http://edu221resources.wikispaces.com/file/view/cooperative_learning_strategies.pdf/426402320/cooperative_learning_strategies.pdfStudents will refer to this link for instructions on how to participate in the Mix-Pair-Freeze activity.
https://www.khanacademy.org/ Students will refer to Khan Academy for additional instruction if needed.
http://linearequationsinreallife.weebly.com/ Students will begin exploring this WebQuest, and working through it individually. This will provide as the final assessment in the unit.
PART II:
Teaching and Learning Sequence(Describe the teaching and learning process using all of the information from part I of the lesson plan)Take all the components and synthesize into a script of what you are doing as the teacher and what the learners are doing throughout the lesson. Need to use all the WHERETO’s. (3-5 pages)
The room will be set up with desks arranged in groups of four, side by side.
Day One: Linear Equations with Properties, and Order of Operations (80 Minutes)
Introduction: Overview of class schedule, and intro of lesson (5 minutes)
(Hook): Start class by telling a story that uses distributive, associative, and commutative properties in real life. (5 Minutes)
Instructional Period: Present Properties, and Order of Operations. Introduce Blogger and show instructional video:
http://www.youtube.com/watch?v=rKVQKQxxUl and have discussion time, to check for understanding for using One Last Question. (25 Minutes)
First Class Activity: Student will work with the Mix-Pair-Freeze cooperative learning activity. They will begin discussing their ides. They will collaborate and decide what they ideas they want to cove in the Blog. (10 Minutes)
Second Class Activity: Students will, in their partners of choice use a Flow chart graphic organizer to come up with several options for their Blogger. They will present a question and work down the steps in the correct order. This will be a good way for them to organize their math questions. (30 Minutes)
Task Introduction: Students will be asked to use Blogger. Upon arriving to the next class they will each share one question they had, as well as where, and how they found the answer. They will also provide one unique thing they have incorporated into their blogs through themes, fonts, back rounds, etc. (5 Minutes)
Day Two: Blogs onLinear Equations with Properties, and the Order of Operations (80 Minutes)
Introduction: The class will briefly review the task assignment to get everyone thinking about their Blogs. Students will all share one thing from their Blog that they learned or liked. Also during this time the teacher will briefly review properties, solutions, and the order of operations. (20 Minutes)
Work Period: Students will work together to create an addition blog entry using properties, and the order of operations. The teacher will roam and help students with question, and give helpful suggestions to each group. (20 Minutes)
Break: Students will take a five-minute break, to socialize and hopefully talk to other piers to compare ideas! The teacher will give students a hint as to collaborate with each other during this time period. (5 Minutes)
Second Work Period: (15Minutes)
Report Out: Students will share their new questions, and answers and provide on example in which it is real world applicable (20 Minutes)
Day 3: Final Assessment Introduction (80 Minutes)
Introduction: Introduce WebQuest, Explain what a WebQuest is and why the students will be participating in one themselves. (15 Minutes)
Hook:Weebly Introduction (5 Minutes)
Exploration and Review: Students will explore the WebQuest and begin to grasp what they will be doing through this Weebly! Students will review previous content, graphic organizers, cooperative learning activities, formative assessments, summative assessments, and other resources. (35 Minutes)
Walk Through: The teacher will walk through the Weebly with the class, and break it down. Questions will be answered and the completion of the WebQuest will begin! (20 Minutes)
Assignment: Students will be asked to download the Google Sketch up program, and begin exploring and playing with some ideas. Also students will look into bridge structures, and come up with some ideas for their 3-Dimensional bridges, Next class the students will continue to work through the Weebly.
The class will be arranged in groups of two. The desks will be placed side-by-side facing the front of the classroom. This will allow for normal instruction, like any other day, but also set allow for an easier transition when groups are formed. Desks will already be in place so the transition time will be far faster. The agenda is pretty simple; it will be made up of three class periods. This first day the teacher will present the lesson on properties, and the order of operations and allow students to chose their own partner. Once in groups the students will watch an intro video on how to use Blogger, and then they will participate in Mix-Pair-Freeze cooperative learning activity, and Flow Chart graphic organizer worksheet. On the second day students will all share one thing that they learned while exploring Blogger technology. A short time will be taken to reteach the content from the previous class, to help struggling students further understand the content. They will then work with their partners to come up with another question to present, and answer using their Blogs. Students will then have a work period. They will be given a break in the middle of the class work period to re motivate themselves. At the end of class, Students will report to the class what their question was, and how they solved it. Finally on the third and last day the students will be introduced to WebQuests. They will be hooked by being introduced to the introduction of the class Weebly. Students will then explore the WebQuest and begin to grasp what they will be doing through this Weebly! Students will review previous content, graphic organizers, cooperative learning activities, formative assessments, summative assessments, and other resources. The teacher will walk through the Weebly with the class, and break it down toward the end of class. Questions will be answered and the completion of the WebQuest will begin! Students will be asked to download the Google Sketch up program, and begin exploring and playing with some ideas. Also students will look into bridge structures, and come up with some ideas for their 3-Dimensional bridges, Next class the students will continue to work through the Weebly.
Where, Why, What, Hook, Tailors:Verbal, Logical/Mathematical, Visual, Musical, Kinesthetic, Intrapersonal, Interpersonal, and Naturalist.
Students will know properties, PMDAS, and solutions. Students will use Mix-Pair-Freeze (Cooperative learning activity) and Flow Chart (Graphic organizer) to start organizing thoughts they have for their Blogs. As the teacher I will deliver a short and to the point instruction of twenty five minutes. In this time I will be able to effectively cover the needed material. Along the way I will ask question to all my students and they will be actively involved by participating in On Last Question. Based on the feedback I receive, I will be able to retouch on certain things and present them in multiple ways until all my students understand each though process. I will easily be able to check for understanding using one last question and I will be able to do it constantly throughout my instructional period. Students can refer back to previous organizers, and learning activities used throughout the unit, and reuse them for assistance while working with the WebQuest. The content of the overall unit is as follows:
Equation: Students may have a general idea of what equations are. An equation is a something that shows, in terms of math, that two things are equal to one another. The statement 60=30+30 is an equation. It is important that students know that both sides of an equation are the same but are simply written in different ways.
Linear equations: are equations that have an unknown variable like (x, y, z), these variables are all of the power 1. This is the most important thing to linear equations. The variable can only be raised to the power of one. A variable to power 2 like (Y2) is not a linear equation because it has an exponent that is not equal to one. 60=20+x is a linear equation.
Irrational Numbers:are numbers that are not integers, whole numbers, or fractions. Instead they are decimals that have an ongoing decimal with NO pattern. For example: 3.3257689475635241639506. There is no pattern therefore it is irrational. The mathematical symbol pi, is a great example of an irrational number.
Rational Numbers: Rational numbers are alike whole numbers, but also include fractions, and decimals. If a decimal has a repeating number such as, 6.6444444444 then it is indeed rational! Repeating decimals are rational, not irrational!
Whole Numbers: wholes numbers are and number that is not a fraction, and is not negative.
Example: {0, 1, 2, 3, 4, 5, .... Infinity}
Integers: Integers are like whole numbers in the fact that they cannot be fractions. They can however be negative.
Example: {Negative Infinity......., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ......... Infinity}
Real Numbers: Real numbers include decimals, fractions, whole numbers, integers, irrational numbers, and rational numbers.
Variables: A variable is an unknown value usually expressed by (x, or y). Knowing that equations are two things that are equal, we sometimes have an unknown value. We express this unknown with a variable. In they equation 4X+ 8= 16, X is our variable.
Constants: constants are numbers with in an equation that stand-alone. In the equation, 12X + 20 = 80, the constants are 20, and 80. 12 is not a constant because it is tied to the X. In this case 12 is considered a coefficient. Constants can also be letters that stand for a fixed number. Most formulas us letters as constants because they can stand for any real number. In the slope-intercept form, Y= mx + b, the constants are Y, and b. m again being tied to a variable (x) is a coefficient.
PMDAS (Order of Operations):
Is also know as please excuse my dear aunt sally. This acronym is a popular way to remember these steps. They stand for doing things in a certain order when solving equations. PMDAS stands for:
1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
Properties:
Commutative:
This property states that you can add or subtract things in any certain order, as well as multiply things in any order.
Examples:
Addition/Subtraction 5 + 8 - 4 = 5 - 4 + 8
Multiplication: 5 x 8 x 4 = 4 x 5 x 8
Associative:
This property states that both multiplication and addition can be two numbers at a time. With addition you can group these numbers in any way, and still get the same answer. With multiplication we can group numbers in a product in any way, and still get the same answer.
Examples:
Addition: (5x + 3x) + 8x = 5x + (8x + 3x)
Multiplication: 2x2(3y) = 3y(2x2)
Distributive:
This property occurs when you are dealing with both multiplication and addition. It tells us that if a term is multiplied by other terms within a set of parenthesis, then we need to "distribute" the multiplying term by all the terms within the parenthesis.
Example: 6(5x + 4)= 30x + 24
Solutions: When dealing with variables that are not to the first power, there may be multiple solutions (answers) for that variable.
Example:
x2-5x +6=0 This reduces to (x - 3) and (x - 2) = 0 which gives us the solutions of x = 3, and x = 2
Inequalities:
An inequality is a mathematical sentence that compares two quantities that do not equal each other, or may possibly equal one another. There are a four main ways to compare quantities:
> (Greater than)
< (Less than)
< (Less than, or equal to)
> (Greater than, or equal to)
An example of this is 20 + 39 < 97-22 This is saying that 20 + 39 is less than 97- 22
To check that this is true, you solve both sides separately which will make this 59 < 65 which saying that 59 is less than 65 which is correct.
Another example of this is 5 x 10 > 32 + 18 this is saying that 5 x 10 is greater than or equal to 32 + 18.
To check this we again solve both sides separately. We get 50 > 50. so in this case they are equal. (50 = 50)
Slope – Intercept Form:
The slope - intercept form of a linear equation is given by the following formula: y= mx + b
‘m’ is the slope and ‘b’ is the y – intercept)
Slope is a ratio use to measure the steepness of a line. To find slope you must find the change in ‘y’ over the change in ‘x’. This can also be written as: Rise/Run
The way to find rise/run is to have to points on a line. For example (5,8) and (10,12); to find the ‘rise’ you find the difference between the y coordinates. So; 12 – 8 = 4 then you do the same thing for the x coordinates to find the ‘run’. So; 10 - 5 = 5 this will make the final answer be 4/5. Our slope is 4/5ths the equation for this is: Y1 - Y / X1- X
Properties of Exponents:
http://hotmath.com/hotmath_help/topics/properties-of-exponents.html
Perimeter: To find the perimeter of a 2D shape you must add up all the sides of that shape. For example, if a rectangle had side lengths of 5, 7, 5, and 7, we would add up every side to get our perimeter. 5+7+5+7= 24. So, the perimeter is 24.
Area: Area is the amount of surface space of a 2D shape. It is measured in square units. The area can me measured in multiple ways such as Centimeters, inches, feet, meters, millimeters, and more.
To find the area we simply multiply the length of a shape by its width. For example if we had a rectangle with a side length of 8 and a width of 12 our area would be 96. We got that by multiplying 8 X 12 = 96
Equip, Explore, Rethink, Tailors:Verbal, Logical/Mathematical, Visual, Musical, Kinesthetic, Intrapersonal, Interpersonal, and Naturalist.
Students will use Mix-Pair-Freeze (Cooperative learning activity) and Flow Chart (Graphic organizer) to start organizing thoughts they have for their Blogs. Students will use these activities for assistance. Their Blog must include the use of properties, and the order of operations. The teacher will use One Last Question to check for understanding. Students will write down one question they have, or something that may be unclear. Students will then use Blogger to create a blog using linear and quadratic equations. Student will spend class time with their partner to work with Blogger. They should be prepared to report their questions and answers at the ends of class. The teacher will roam the classroom providing answers to questions and helping students with their Blogs. Students must collaborate their ideas with the teachers before full creation, and presentation. Students will both help to come up with ideas, during the creation of math problems using properties, order of operations, and they will both help to creatively incorporate it all into Blogger. On the third day students will be introduced to WebQuests. During this class period students will tie up loose ends with their Blogs, and begin reviewing, recalling, and rethinking about all the things that were covered in this unit. They can refer to the process section of the Weebly to achieve this.
Explore, Experience, Revise, Rethink, Refine, Tailors: Verbal, Logical/Mathematical, Visual, Musical, Kinesthetic, Intrapersonal, Interpersonal, and Naturalist.
Students will self-assess during their rethink/ refine stage in the final assessment. They will go down through the rubrics that they have been given. They will grade themselves, and add or fix anything that they missed or feel they may improve on. During the class presentations I will grade them on the same rubrics. I will also grade them based on the effort, participation, and quality of their work. At the end of all the presentations I will hand back these checklists along with a small written reflection. They will all receive their grades immediately after all the gallery walk is over. I will address the class overall and then talk to each group that has questions or comments. This will all pertain to their homework because they will be given problems from their book on the exact same material. In the following classes they will be given a pre- quiz, and finally a quiz. This lesson content will combine with other contents, and students will be assessed on multiple lesson contents at the end of the unit.
Evaluate, Tailors: Verbal, Interpersonal, Intrapersonal, Logical
Content Notes
Students will know….
Develop detailed content notes so a substitute or a colleague can teach your lesson. (2-3 pages)
Equation: Students may have a general idea of what equations are. An equation is a something that shows, in terms of math, that two things are equal to one another. The statement 60=30+30 is an equation. It is important that students know that both sides of an equation are the same but are simply written in different ways.
Linear equations: are equations that have an unknown variable like (x, y, z), these variables are all of the power 1. This is the most important thing to linear equations. The variable can only be raised to the power of one. A variable to power 2 like (Y2) is not a linear equation because it has an exponent that is not equal to one. 60=20+x is a linear equation.
Irrational Numbers:are numbers that are not integers, whole numbers, or fractions. Instead they are decimals that have an ongoing decimal with NO pattern. For example: 3.3257689475635241639506. There is no pattern therefore it is irrational. The mathematical symbol pi, is a great example of an irrational number.
Rational Numbers: Rational numbers are alike whole numbers, but also include fractions, and decimals. If a decimal has a repeating number such as, 6.6444444444 then it is indeed rational! Repeating decimals are rational, not irrational!
Whole Numbers: wholes numbers are and number that is not a fraction, and is not negative.
Example: {0, 1, 2, 3, 4, 5, .... Infinity}
Integers: Integers are like whole numbers in the fact that they cannot be fractions. They can however be negative.
Example: {Negative Infinity......., -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5, ......... Infinity}
Real Numbers: Real numbers include decimals, fractions, whole numbers, integers, irrational numbers, and rational numbers.
Variables: A variable is an unknown value usually expressed by (x, or y). Knowing that equations are two things that are equal, we sometimes have an unknown value. We express this unknown with a variable. In they equation 4X+ 8= 16, X is our variable.
Constants: constants are numbers with in an equation that stand-alone. In the equation, 12X + 20 = 80, the constants are 20, and 80. 12 is not a constant because it is tied to the X. In this case 12 is considered a coefficient. Constants can also be letters that stand for a fixed number. Most formulas us letters as constants because they can stand for any real number. In the slope-intercept form, Y= mx + b, the constants are Y, and b. m again being tied to a variable (x) is a coefficient.
PMDAS (Order of Operations):
Is also know as please excuse my dear aunt sally. This acronym is a popular way to remember these steps. They stand for doing things in a certain order when solving equations. PMDAS stands for:
1. Parentheses
2. Exponents
3. Multiplication
4. Division
5. Addition
6. Subtraction
Properties:
Commutative:
This property states that you can add or subtract things in any certain order, as well as multiply things in any order.
Examples:
Addition/Subtraction 5 + 8 - 4 = 5 - 4 + 8
Multiplication: 5 x 8 x 4 = 4 x 5 x 8
Associative:
This property states that both multiplication and addition can be two numbers at a time. With addition you can group these numbers in any way, and still get the same answer. With multiplication we can group numbers in a product in any way, and still get the same answer.
Examples:
Addition: (5x + 3x) + 8x = 5x + (8x + 3x)
Multiplication: 2x2(3y) = 3y(2x2)
Distributive:
This property occurs when you are dealing with both multiplication and addition. It tells us that if a term is multiplied by other terms within a set of parenthesis, then we need to "distribute" the multiplying term by all the terms within the parenthesis.
Example: 6(5x + 4)= 30x + 24
Solutions: When dealing with variables that are not to the first power, there may be multiple solutions (answers) for that variable.
Example:
x2-5x +6=0 This reduces to (x - 3) and (x - 2) = 0 which gives us the solutions of x = 3, and x = 2
Inequalities:
An inequality is a mathematical sentence that compares two quantities that do not equal each other, or may possibly equal one another. There are a four main ways to compare quantities:
> (Greater than)
< (Less than)
< (Less than, or equal to)
> (Greater than, or equal to)
An example of this is 20 + 39 < 97-22 This is saying that 20 + 39 is less than 97- 22
To check that this is true, you solve both sides separately which will make this 59 < 65 which saying that 59 is less than 65 which is correct.
Another example of this is 5 x 10 > 32 + 18 this is saying that 5 x 10 is greater than or equal to 32 + 18.
To check this we again solve both sides separately. We get 50 > 50. so in this case they are equal. (50 = 50)
Slope – Intercept Form:
The slope - intercept form of a linear equation is given by the following formula: y= mx + b
‘m’ is the slope and ‘b’ is the y – intercept)
Slope is a ratio use to measure the steepness of a line. To find slope you must find the change in ‘y’ over the change in ‘x’. This can also be written as: Rise/Run
The way to find rise/run is to have to points on a line. For example (5,8) and (10,12); to find the ‘rise’ you find the difference between the y coordinates. So; 12 – 8 = 4 then you do the same thing for the x coordinates to find the ‘run’. So; 10 - 5 = 5 this will make the final answer be 4/5. Our slope is 4/5ths the equation for this is: Y1 - Y / X1- X
Properties of Exponents:
http://hotmath.com/hotmath_help/topics/properties-of-exponents.html
Perimeter: To find the perimeter of a 2D shape you must add up all the sides of that shape. For example, if a rectangle had side lengths of 5, 7, 5, and 7, we would add up every side to get our perimeter. 5+7+5+7= 24. So, the perimeter is 24.
Area: Area is the amount of surface space of a 2D shape. It is measured in square units. The area can me measured in multiple ways such as Centimeters, inches, feet, meters, millimeters, and more.
To find the area we simply multiply the length of a shape by its width. For example if we had a rectangle with a side length of 8 and a width of 12 our area would be 96. We got that by multiplying 8 X 12 = 96
Handouts
List the items that need to be printed out for the lesson.
Rubrics for WebQuest (60 copies)
Flow Chart graphic organizer (60 copies front and back)
ALL OTHER HANDOUTS CAN BE FOUNF ON THE WEBQUEST.
Maine Common Core Teaching Standards for Initial Teacher Certification and Rationale
Standard 1 –Learner Development. The teacher understands how learners grow and develop,recognizing that patterns of learning and development vary individually within and across the cognitive, linguistic, social, emotional, and physical areas, and designs and implements developmentally appropriate and challenging learning experiences.
Learning Styles
Clipboard: The clipboard students in my class will have graphic organizers in order to help the students organize step-by-step their logic and ideas. The class period is clearly planned out on the board so students can see how long we will be doing each thing in class. Students will be given a handout, and rubrics that will provide my expectations. This will help them to understand exactly what they are to do.
Microscope: The microscopes in my class will be able to have in depth conversations while they create their final products using all the content from the unit. They will be able to solve problems alike in their textbooks, which will further expand their understandings.
Puppy: For my puppy student I will ensure that they are receiving extra supportive and assistance from myself to make thing more easy going. This will help them feel like they are working and learning in a fun, and safe environment. These students will be able to collaborate with their peers in the classroom as well. The students will have multiple planned times to meet with me and talk about the project.
Beach Ball: For my beach ball learners I will provide them with options, and let them use whatever tools they feel will help them complete the project. Students will be placed with another student who will likely motivate and interest their partner while using Blogger, and Google SketchUp technology. They will be able to present one section of their final product if they desire and present the rest to the teacher at another time. All the beach ball learners will participate in cooperative learning activities, and graphic organizers with their partners. Here they will be heard, and they will feel as if they can speak freely.
Rationale: Students will be able to experience all of the learning styles in this project. Students and the teacher will realize how other students need information, or even that some students require a higher comfort level. This will allow for a judge free, respectful classroom for all students so that they can reach their highest abilities.
Standard 6 -Assessment. The teacher understands and uses multiple methods of assessment to engage learners in their on growth,to monitor learner progress, and to guide the teacher's and learner's decision making.
Formative (Assessment for Learning)
Section I – checking for understanding during instruction
Students will ask one last question before leaving class. They will be asked to post this question in their blog. They will first present the question, and then try to answer is. Students are encouraged to use any resource needed to answer this question. Next class, students will report out their question, and their answer.
Section II – timely feedback for products (self, peer, teacher)
Students will then use Blogger to first present their question, and second to answer that question involving the order of operations and the three properties. Students will spend time collaborating with their classmates, and having discussions about their questions, and answers.
Summative (Assessment of Learning):
Blogger: Students will discuss and reflect on questions they may have remaining from class. Students will then post a blog entry using Blogger technology. They will post their questions on Blogger, and attempt to answer their own question using multiple resources. These resources are limitless. The web, parents, textbook, friends, or maybe even another teacher, are good reference ideas. This will be an ongoing project throughout the unit. You will be graded on your participation, and work ethic. (40 Points)
Standard 7-Planning Instruction. The teacher plans instruction that supports every student in meeting rigorous learning goals by drawing upon knowledge of content areas, curriculum,cross-disciplinary skills, and pedagogy, as well as knowledge of learners and the community context.
Content Knowledge:
See Content Notes
MLR or CCSS:
Common Core State Standards:
Content Area: Algebra
Grade Level: High School
Domain: Creating Equations
Cluster: Create equations that describe numbers or relationships.
Standards(s): 1. Create equations and inequalities in one variable and use them to solve problems.
Facet: Empathy, Explanation, Application, Perspective, Interpretation, and Self-Knowledge
Rationale:
Student will meet this standard by applying real world applications. With these applications they will create equations and inequalities with the use of:
Standard 8 -Instructional Strategies. The teacher understands and uses a variety of instructional strategies to encourage learners to develop deep understanding of content areas and their connections, and to build skills to apply knowledge in meaningful ways.
MI Strategies:
Verbal: Students will verbally tell the teacher their One Last Question before leaving class. This question should relate to one of the three properties: distributive, associative, or commutative.
Logic: Student will be forced to really think about their question relating to one of the three properties: distributive, associative, or commutative in a blog entry on Blogger.
Visual: The teacher will visually show PMDAS during class to help students further understand the three properties: distributive, associative, or commutative.
Intrapersonal: Student will individually work on their blog entry as homework. Here they will present a question on one of the three properties: distributive, associative, or commutative and try to answer their own question prior to the next class period.
Interpersonal: Students will interact with a friend, parent, or even another teacher to try and find the answer to their question relating to one of the three properties: distributive, associative, or commutative.
Naturalist: In the blogs, students will be encouraged to create a story, in nature using the three properties.
Type II Technology:
Blogger will be used as the technology in this lesson. Blogger is an online blog platform run by Google. Blogger is completely free and can be run through any Google account. In this case students will create a blog as a reflection tool. They will be able to create their layout, and page setups. Their first blog will incorporate a question and answer based on PMDAS (the order of operations) or on one of the three properties (associative, commutative, and distributive). This is a type two technology because Blogger has amazing capabilities. Blogger can present materials in cool, colorful, and individual ways. It creates a sense of structured flow for the students. Students will benefit from Blogger technology because it will allow them to be creative, and they will have the opportunity to work at their own pace, and own ability. Students will be given the opportunity to think, analyze, and present their Blog reflections on the topic of PMDAS (the order of operations) and the three properties (associative, commutative, and distributive)
Rationale:
This lesson was designed in such a way where differentiation can be used, to fit the needs of all students. All Multiple Intelligences were kept in mind during the process, and resources are provided for the students. During this lesson students will be able to work their strong intelligences as well as work on some of their weaker ones. They will also be able to use the technology, and multiple resources to the advantage of helping them to reach a higher, more enjoyable learning level.
NETS STANDARDS FOR TEACHERS
1. Facilitates and Inspire Student Learning and Creativity. Teachers use their knowledge of subject matter, teaching and learning, and technology to facilitate experiences that advance student learning, creativity, and innovation in both face-to-face and virtual environments.
a. Promote, support, and model creative and innovative thinking and inventiveness
b. Engage students in exploring real-world issues and solving authentic problems using digital tools and resources
c. Promote student reflection using collaborative tools to reveal and clarify students’ conceptual understanding and thinking, planning, and creative processes
d. Model collaborative knowledge construction by engaging in learning with students, colleagues, and others in face-to-face and virtual environments
Rationale:
Students will be working with Blogger and Google SketchUp in order to create a new way to ask and answer questions, and create 3-Dimensional structures using mathematics. Students can use this technology to share information with their peers while working. The lesson is geared to the fact that students will be working together in order to understand the information. Two brains are better than one. This will help the overall learning and progress of the students. Students will also be learning the content material through repetition, and applying that knowledge when using Blogger and Google SketchUp.
2. Design and Develop Digital Age Learning Experiences and Assessments. Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop knowledge, skills, and attitudes identified in the NETS-S.
a. Design or adapt relevant learning experiences that incorporate digital tools and resources to promote student learning and creativity
b. Develop technology-enriched learning environments that enable all students to pursue their individual curiosities and become active participants in setting their own educational goals, managing their own learning, and assessing their own progress
c. Customize and personalize learning activities to address students’ diverse learning styles, working strategies, and abilities using digital tools and resources
d. Provide students with multiple and varied formative and summative assessments aligned with content and technology standards and use resulting data to inform learning and teaching
Rationale:
Students will be using Blogger and Google SketchUp as a way to explore new intelligences and build further on their stronger intelligences. Students will have opportunities to relate information to their learning style of choice, whether it is interpersonal, intrapersonal, visual, or even logic. They will have opportunities to work in groups, and individually. A number of tasks and activities will be given to the students to help them understand the information. They will be able to practice, use graphic organizers, rubrics, cooperative learning activities, and will have multiple chances to meet with the teacher and collaborate with their peers. They will have a final product that they will present to the class, which will show whether or not the student has mastered the material.